``our system''

Project on Force Evaporation cooling in 40K

15/3/2016

In ultracold atoms we must reach a temperature of the order of 30 nk. By laser cooling techniques we are limited by the rate of heating of the atom by the light, around 30 μk .

Thus was developed the method of Evaporative cooling. The principle of this method is to remove atoms fastest (high energy) and by this dramatically lower the temperature of each ensemble.

The force on atom in a magnetic trap is

F = − μbmjgj(dB0(z))/(dz)

We do this for atoms in a state of |9 ⁄ 2, 9 ⁄ 2⟩. If we can give it enough energy so it could switch to a different spin and if we were to switch to a diffrent ml it would feel a upside down potential and therefore would not be in a potential well, as a free particle.

Due to the exerted magnetic field the energy levels in atoms are split

Figure 1 Hyperfine energy shift for the D1manifold (2P1 ⁄ 2) of 40K as a function of magnetic field

Zeeman shift makes the energy required to stimulate and create an atomic transition to be:

So if we give the atom enough energy of the appropriate frequency, the atom will then transition to |7 ⁄ 2, 7 ⁄ 2⟩ . Then the atom will be free and will not be placed in our atoms cloud (and actually go out of our ensemble).Then we can calculate the change in the number of atoms and internal energy by:

dN = (1)/(2λ(ℏωr)3)∞⌠⌡Ec(ϵ2)/(e(ϵ)/(kT) + 1)dϵ

dU = (1)/(2λ(ℏωr)3)∞⌠⌡Ec(ϵ3)/(e(ϵ)/(kT) + 1)dϵ

where ωr are oscillator frequencies of the laser and λ = (ωz)/(ωr) .

So if we divide the process into segments of time and each segment is considered how many atoms and energy got lost we can find the number of atoms and the temperature at the end of the process.

The program runs in MATHEMATICA 10, you can download it
here.
At the Technion there is MATHEMATICA 10 on all the computers. If you have a problem to get it you can ask help from the computer center here .
To run the program you need to choose Evaluation-evaluate Notebook.
For more details go to MATHEMATICA home page here .
if you want to change something you can do it but then run all the notebook again.